Hermitian dynamics in a class of pseudo-Hermitian networks

TL;DR

This paper explores how certain pseudo-Hermitian lattice systems can exhibit Hermitian dynamics through specific superpositions of eigenmodes, demonstrated in an exactly solvable PT-symmetric ladder model.

Contribution

It establishes a connection between pseudo-Hermitian and Hermitian descriptions in lattice systems, showing conditions under which non-Hermitian systems behave Hermitian.

Findings

Pseudo-Hermitian clusters can produce Hermitian dynamics via superpositions.

Hermitian behavior persists with multiple eigenmodes under certain restrictions.

Demonstrated in an exactly solvable PT-symmetric ladder system.

Abstract

We investigate the connection between pseudo-Hermitian and Hermitian descriptions for a lattice, which consists of a set of isomorphic pseudo-Hermitian clusters. We show that such non-Hermitian systems can act as Hermitian systems. This is made possible by considering the dynamics of a state involving the superposition of a single eigenmode of each isomorphic clusters. It still holds when multiple eigenmodes are involved when additional restriction on the state is imposed. This Hermitian dynamics is demonstrated for the case of an exactly solvable PT-symmetric ladder system.